Although we focus on the HDP, the model could be extended to hierarchical processes based on priors beyond the DP, such as the hierarchical Pitman-Yor process [1]} or more generally hierarchical normalized random measures [2]}. An investigation and comparison of the induced prior distribution over the clustering structure and number of clusters, both within and between datasets, is provided in [3]}. Moreover, the MCMC algorithm developed here can be extended based on finite-dimensions approximations of normalized random measures [4]}. Other potential model extensions include cluster-specific mean-dispersion relationships for increased flexibility.
